Thread: explain why these two expressions are equal

sin(9pi/7) = -sin(2pi/7)

Stuck....

Step by step would be appreciated very much.

Thanks

note ...



... now use the sum identity for sine

If you draw the terminal angles and on a unit circle, you will see that they differ by . The sine of the angle is the y-coordinate of that angle/point on the unit circle. You will see that one is the negative of the other.

In general, .

Originally Posted by skeeter

note ...



... now use the sum identity for sine

Why use the sum identity? You already have it in the form .

Originally Posted by Prove It

Why use the sum identity? You already have it in the form .

so, you assume the OP is familiar with that specific identity derived from the sum identity?

Originally Posted by skeeter

so, you assume the OP is familiar with that specific identity derived from the sum identity?

While that identity can be derived from the sum identity, it is also blatantly obvious from the unit circle.

Originally Posted by Prove It

While that identity can be derived from the sum identity, it is also blatantly obvious from the unit circle.

"blatantly obvious from the unit circle" ... thanks for the lesson.

i am appreciate you ... this is right .... work smart not hard...

\sin\left(\frac{9\pi}{7}\right) = \sin\left(\pi + \frac{2\pi}{7}\right)